   Chapter 12.2, Problem 15E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the integrals in Problems 7-36. Check your results by differentiation. ∫ 8 x 5 ( 4 x 6 + 15 ) − 3 d x

To determine

To calculate: The value of the integral 8x5(4x6+15)3dx.

Explanation

Given Information:

The provided integral is 8x5(4x6+15)3dx

Formula used:

The power formula of integrals:

undu=un+1n+1+C (forn1)

The power rule of differentiation:

ddu(un)=nun1

Calculation:

Consider the provided integral:

8x5(4x6+15)3dx

Rewrite the integral by multiplying and dividing by 3 as:

1324x5(4x6+15)3dx

Let u=4x6+15, then derivative will be,

du=d(4x6+15)=24x5dx

Substitute du for 24x5dx and u for 4x6+15 in provided integration.

1324x5(4x6+15)3dx=13u3du

Now apply, the power formula of integrals:

undu=un+1n+1+C

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